APPENDIX 



687 



which represent class marks lay off lines parallel to the j-axis and of 

 lengths corresponding to the various frequencies, according to the scale on 

 the j-axis. When this is done there will be a series of parallel lines at 

 equal distances apart, all perpendicular to the .r-axis and parallel to the 

 j-axis, but of lengths corresponding to the various frequencies and therefore 

 unequal. Joining the tops of the lines so constructed by straight lines 

 gives the frequency polygon shown in Fig. I. The tops of the lines thus 

 joined give an orderly arrangement of points, through which it may be 

 possible to draw a smooth curve. If it is impossible to draw a smooth curve 

 through all of them, draw a smooth curve as near as possible to all of them. 

 The curve so drawn is called a frequency curve (not shown in figure). 



r 



O'JE 



ll'U 



"l-P 



71 



4 4.5 5 5.5 -6 6.5 7 7.5 8 8.5 9 9.5 10 



FIG. i 



Any point P in the plane represents two numbers : the one number is 

 represented by the distance of the point from the_y-axis, and the other by 

 its distance from the .r-axis. The number which gives the distance of P from 

 the j-axis is called the abscissa of P, and the number which gives its distance 

 from the ^r-axis is called its ordinate. . The two numbers together are often 

 spoken of as the coordinates of the point P. 



Significance of area under curve. Construct rectangles such as ABCD 

 and BC ' EF on the ordinates at class marks as mid-lines, making the sides 

 AD, BC, etc., bisect the class intervals along the .r-axis. Suppose, now, 

 that we define unit area as a rectangle bounded by AB, AD, BC, and a 

 line parallel to AB and just far enough from it so that the distance 

 between AB and this line represents unit frequency. Then the area of 

 ABCD is 1 10, and the area of all such rectangles taken together is equal 

 numerically to the total population. In drawing the smooth curve men- 

 tioned above, we should aim to make the area between the curve the 



